Moto G is an Android smartphone that does not have a microSD slot. So, the storage of the smartphone cannot be extended. If you want to transfer files between your Ubuntu computer and the Moto G, there are 3 possible ways to do that: FTP over wireless, PTP over USB and MTP over USB.

If your Ubuntu computer has wireless, I highly recommend using FTP over wireless. It is convenient (no wires!), offers good transfer speed and the entire /sdcard contents are available for read and write.

If your Ubuntu computer does not have wireless, then your next option is to use a micro-USB-to-USB cable. The choices here are PTP and MTP. You can enable and switch between the two after you connect Moto G to your computer using a USB cable. If you enable PTP, then Moto G is automatically mounted as a partition in Nautilus. However, you will only be able to see the /sdcard/DCIM and /sdcard/Pictures directories. If you are transferring photos, then this option offers good transfer speed.

If your Ubuntu computer does not have wireless and you still want to read and write to the contents of /sdcard then the option left to you is MTP. Note that with MTP, Moto G takes a really long time to mount and the transfer speeds are really really low. It can take ages to transfer even a small file. You have been warned! :-)

There are many solutions offered online to mount the contents of /sdcard using MTP. This solution is the only one that worked for me:

Install the MTP packages:

$ sudo apt-get install mtp-tools mtpfs

Connect Moto G using a USB cable to your computer. Make sure MTP is selected, and not PTP.

Find out the vendor ID and product ID of Moto G using mtp-detect. For my smartphone I got: